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Some insurance brokers are ok with >40 yr old 'historic' vehicles without MOT (form V 112 when it comes to rubber stamping the zero rated road tax) - possibly more so if you're outside London?
I've used Peter James Insurance for many years for a couple of 1950s mopeds - seems fine so far, but then I haven't made any claims.Edit - possibly this should have been a reply to @n3il ? FWIW I'm in rural Shropshire, possibly comparable to rural Wales for insurance purposes.
Looking at a four stroke as a two stroke may have issues with crank seals if left sitting.
MOT wise insurance companies like to see the vehicle is roadworthy easiest way is to have an MOT.
Honda xl185? Have had issues with points if the bike has been siting for sometime. But might be easier to get a dr350 and use fuel stabilizer as modern stuff goes gummy quite quickly.